# Point A is at (-6 ,1 ) and point B is at (2 ,8 ). Point A is rotated (3pi)/2  clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

Jul 31, 2018

color(green)("Change in dist. due to the rotation" = sqrt113 - sqrt65 ~~ 1.3185

#### Explanation:

$A \left(- 6 , 1\right) , B \left(2 , 8\right) , \text{ rotated about origin by " (3pi)/2 " clockwise}$

$A \left(- 6 , 1\right) \to A ' \left(- 1 , - 6\right)$

$B \left(2 , 8\right) \to B ' \left(- 8 , 2\right)$

$\text{Distance } \overline{A B} = \sqrt{{\left(- 6 - 2\right)}^{2} + {\left(1 - 2\right)}^{2}} = \sqrt{65}$

$\text{Distance } \overline{A ' B '} = \sqrt{{\left(- 1 - - 8\right)}^{2} + {\left(- 6 - 2\right)}^{2}} = \sqrt{113}$

color(green)("Change in dist. due to the rotation" = sqrt113 - sqrt65 ~~ 1.3185#